Karhunen-Loeve expansion of Spartan spatial random fields

Random fields (RFs) are important tools for modeling space-time processes and data. The Karhunen-Loeve (K-L) expansion provides optimal bases which reduce the dimensionality of random field representations. However, explicit expressions for K-L expansions only exist for a few, one-dimensional, two-parameter covariance functions. In this paper we derive the K-L expansion of the so-called Spartan spatial random fields (SSRFs). SSRF covariance functions involve three parameters including a rigidity coefficient eta(1) a scale coefficient, and a characteristic length. SSRF covariances include both monotonically decaying and damped oscillatory functions; the latter are obtained for negative values of eta(1). We obtain the eigenvalues and eigenfunctions of the SSRF K-L expansion by solving the associated homogeneous Fredholm equation of the second kind which leads to a fourth order linear ordinary differential equation. We investigate the properties of the solutions, we use the derived K-L base to simulate SSRF realizations, and we calculate approximation errors due to truncation of the K-L series. (C) 2015 Elsevier Ltd. All rights reserved.